Democrats rallied behind President Barack Obama’s decision to allow insurers to offer health-insurance policies next year that otherwise would have been canceled, and his mea culpa before a televised audience quelled a brewing rebellion among congressional Democrats.

While Republicans continued to criticize Mr. Obama, Democrats said that the president’s move was a practical answer to a growing a political problem. Democrats seemed to calm down as much because of Mr. Obama’s show of contrition as because he took action to restore canceled policies.

“The concern was that there were a lot of problems and the administration wasn’t adequately acknowledging them and accepting accountability and responsibility to fix them,” said Rep. Jim Moran (D., Va.) after a briefing with White House officials. “I think that’s changed to a large extent with the president’s statement today.”

“Most people feel like they’ve kind of turned a corner as far as accepting some responsibility and offering something,” said Rep. Steve Cohen (D., Tenn.)

The comments came as insurers said that they were concerned about Mr. Obama’s decision, warning it was unclear how the changes could be put into effect. With many lawmakers still weighing the developments, it was unclear whether the insurance industry’s reaction would prove to be a new political sticking point.

The White House acted one day before a Friday vote in the House of Representatives on allowing insurers to offer policies next year that are slated to be discontinued. House Democratic leaders are urging rank-and-file lawmakers to vote against the Republican plan, from Rep. Fred Upton (R., Mich.) But without an alternative, many House Democrats had begun to signal they would vote for Mr. Upton’s bill, in a rebuke to Mr. Obama. Many Democrats believe Mr. Upton’s bill is another way to undermine the Affordable Care Act, because it would open up sales of policies that don’t meet the law’s standards to new customers instead of limiting sales to existing customers.

Speaker John Boehner (R. Ohio) said he would press ahead with plans to have the House vote Friday on legislation designed to address the issue and said he was “highly skeptical’’ that Mr. Obama could solve it administratively.

But Mr. Boehner argued that the effort to fix that particular problem in the roll out of the health law did not deter Republicans from their longstanding effort to repeal the law entirely.

Republicans streamed to the House floor to share details of constituents whose health plans were being canceled.

But Mr. Obama’s decision and statements appeared to take the sting of the criticisms for Democrats.

Rep. Juan Vargas (D., Calif.) said the president took a good first step, and while more legislation was needed, said he would oppose Mr. Upton’s bill on Friday and predicted most Democrats would.

Democrats who had supported such legislation, such as one introduced by Sen. Mary Landrieu (D., La.), welcomed Mr. Obama’s move, although they said that more may have to be done legislatively, depending on how effective his administration action proves to be.

“I think the president’s proposal is a constructive first step,” said Sen. Richard Blumenthal (D., Conn.). “But it’s only a first step.”

Senate Majority Leader Harry Reid (D.,Nev.) said he was prepared to move legislation if necessary, but signaled no immediate plans to do so.

“The fix proposed by President Obama today is an important step towards addressing a problem that has arisen and if we need to do more, we will,” Mr. Reid said.

Even Democrats up for re-election in 2014, who were among those who stand to lose most politically from backlash against the health, offered qualified support for the Obama decision.

“It doesn’t go as far as I’d like it to go, but it’s certainly a step in the right direction,” said Sen. Jeff Merkley (D., Ore.), who has been one of the most vocal critics of the Obama administration’s handling of the health-law rollout. He said that he was concerned that the fix would only last one year, noting the concept was that people could keep their existing plans.

Democrats said they were relieved that Mr. Obama had chosen to act using his executive powers, instead of leaving it up to Congress, where it is easier to block legislation than to pass it.

Sen. Chuck Schumer (D., N.Y.) said the president did “exactly the right thing” by acting administratively because that is the only practical option “so long as the House is intent on undoing Obamacare one way or another.”

A Senate Democratic leadership aide said that Democrats may want to bring up further legislation even if it is doomed to fail to “let people go on record for doing something.’’

“This is the beginning of turning the battleship around,’’ said the aide. “This could be the beginning of the end of the bad news’’ with regard to the health care law rollout.

About Washington Wire

Washington Wire is one of the oldest standing features in American journalism. Since the Wire launched on Sept. 20, 1940, the Journal has offered readers an informal look at the capital. Now online, the Wire provides a succession of glimpses at what’s happening behind hot stories and warnings of what to watch for in the days ahead. The Wire is led by Reid J. Epstein, with contributions from the rest of the bureau. Washington Wire now also includes Think Tank, our home for outside analysis from policy and political thinkers.